DENVER (AP) — Mitt Romney basked in rave reviews Thursday after his first debate with President Barack Obama, envisioning an inaugural celebration with conservative activists, while Obama tried to rebound by telling his rival, “If you want to be president, you owe the American people the truth.”

Obama’s remarks at a Colorado campaign event were a sharp contrast to his uncomfortable, low-energy appearance Wednesday night, where Romney’s assertive performance was aimed at reversing his slipping stance in the polls. Republicans who had despaired before the debate quickly rallied to Romney’s side.

Obama’s campaign on Thursday promised “adjustments” would be made.

And Obama appeared to wake up Thursday, attacking Romney for offering plans to fix the still-weak economy without saying how he would do it.

“The man on stage last night doesn’t want to be held to account … for what he’s been selling for the last year,” Obama said. He added, “Here’s the truth: Gov. Romney cannot pay for his $5 trillion tax plan without blowing up the deficit or sticking it to the middle class.”

It wasn’t clear whether the debate would sway the less than 10 percent of Americans who say they haven’t yet decided on a candidate. And two debates remain before the Nov. 6 election. Both candidates quickly returned to campaigning Thursday in the handful of states that will determine the next president.

Romney said the election will be a “close-fought battle” as he made an unscheduled appearance at a conservative gathering in Colorado, where he took the stage to sustained cheers.

“You guys are going to have to cheer here, and then go out and knock on doors, and get people who voted for President Obama to see the light and come join our team,” Romney said. “And if you do that, we’ll all be able to come together and have a wonderful inauguration celebration in January. So let’s make sure that happens.”

Obama campaign strategist David Axelrod told reporters that the president is “eager” for the next debate. “I’m sure that we will make adjustments,” Alexrod added.

Axelrod also repeatedly accused Romney of “hiding the truth and the facts” from the American people.

Romney campaign spokeswoman Amanda Henneberg responded to the accusations by saying the Obama campaign “offered no defense of the president’s first term record or vision for a second term, and instead, offered nothing but false attacks, petulant statements, and lies about Gov. Romney’s record.”

As Romney faced the president directly for the first time in the campaign, signs already were indicating that the race was tightening in some of those battleground states where Obama has enjoyed a recent advantage. The election is decided in state-by-state contests and not by popular vote.

Obama, who appeared to spend much of the 90 minutes looking at the podium while Romney looked at him, signaled that he won’t let up on his message that Romney’s plans on taxes, health care, the deficit and more just don’t add up.

“It’s arithmetic,” said Obama, hammering at Romney’s conspicuous lack of details with far less enthusiasm.

Both candidates came into a newly structured debate with distinct missions and largely achieved them. Romney needed to project leadership and dispel the image of an out-of-touch multimillionaire. Obama needed to avoid making any major mistakes and press the case that he still has more to offer to improve an economy that continues to sag.

Notably, Obama made no mention of Romney’s secretly recorded remark that he’s not worried about the 47 percent of Americans who don’t pay taxes. Democratic ads, though, have been using the comment heavily since it emerged last month.

Asked why the president didn’t raise the video, Axelrod suggested to MSNBC that he didn’t need to since it has been so widely seen and heard. “The president’s belief is that’s something that has been very much a part of the discussion,” Axelrod said.

Ed Gillespie, a top aide to Romney, told NBC that what people saw in the debate was a presidential challenger “who had a command of the facts.”

Both political parties released sharp videos Thursday playing off the debate, with Republicans calling theirs “Smirk” and focusing on Obama’s sometimes sour-looking demeanor. The Democrats called theirs “Mitt Romney: What a Guy,” showing Romney repeatedly interrupting the moderator.

Two debates remain, on Oct. 16 and Oct. 22. The second will focus on foreign affairs.

The campaigns now head to some of the most hotly contested states over the next few days. Obama was staying in Colorado on Thursday, while Romney headed to Virginia.

In next few weeks, Romney is expected to give a number of speeches filling in details to answer criticism that he hasn’t clearly outlined his plans. The Republican challenger begins with a foreign policy speech in Virginia on Monday. Subsequent speeches are expected to focus on job creation, debt and spending.

Romney has promised to balance the budget in eight years to 10 years but hasn’t explained just how he’ll do it.

“At some point, I think the American people have to ask themselves, is the reason that Governor Romney is keeping all these plans to replace secret because they’re too good?” Obama said, in a rare show of passion. “Is it because that somehow middle-class families are going to benefit too much from them? No.”

The president said the U.S., with its still-weak economy and unemployment above 8 percent, faces tough problems that defy simple solutions and said his own choices were “benefiting middle-class families all across the country.”

Romney maintained it was Obama who was crushing the middle class and getting the numbers wrong, telling him, “Mr. President, you’re entitled to your own airplane and your own house, but not your own facts.”